What are the initial and maintenance margin on account

Question

Assignment:

Question 1. Margin Account and Settlement

Suppose that you bought two one-year gold futures contracts when the one-year futures price of gold was US$1,340.30 per troy ounce. You then closed the position at the end of the sixth trading day. The initial margin requirement is US$5,940 per contract, and the maintenance margin requirement is US$5,400 per contract. One contract is for 100 troy ounces of gold. The daily prices on the intervening trading days are shown in the following table.

Day	Settlement Price
0	1340.30
1	1345.50
2	1339.20
3	1330.60
4	1327.70
5	1337.70
6	1340.60

Assume that you deposit the initial margin and do not withdraw the excess on any given day. Whenever a margin call occurs on Day t, you would make a deposit to bring the balance up to meet the initial margin requirement at the start of trading on Day t+1, i.e., the next day.

a. What are the initial margin and maintenance margin on your margin account?

b. Fill the appropriate numbers in the blank cells in the following table. (Hint: See solution to Q19 in Lesson 2 Learning Activity.

Day	Settlement price per troy ounce	Mark-to-Market	Other Entries	Account Balance	Explanation	Margin Call? Y/N
0	$1340.30
1	$1345.50
2	$1339.20
3	$1330.60
4	$1327.70
5	$1337.70
6	$1340.60

c. What is your total profit after you closed out your position?

Question 2. Binomial Model and Option Pricing

The shares of XYZ Inc. are currently selling for $120 per share. The shares are expected to go up by 10 percent or down by 5 percent in each of the following two months (Month 1 and Month 2). XYZ Inc. is also expected to pay a dividend yield of 2 percent at the end of Month 1. The risk-free rate is 0.5 percent per month.

a. What is the value of an American call option on XYZ shares, with an exercise price of $125 and two months to expiration? Use the binomial model to obtain the answer.

b. Draw a binomial tree diagram for this American call option, showing the share price, call price, and whether the call should be exercised at each state during the next two months.

Question 3. Currency Option Pricing with Binomial Model

On January 11, the spot exchange rate for the U.S. dollar is $0.70 per Canadian dollar. In one year's time, the Canadian dollar is expected to appreciate by 20 percent or depreciate by 15 percent. We have a European put option on U.S. dollars expiring in one year, with an exercise price of 1.39 CND$/US$, that is currently selling for a price of $2.93. Each put option gives the holder the right to sell 10,000 U.S. dollars. The current one-year Canadian Treasury Bill rate is 2 percent, while the one-year U.S. Treasury Bill rate is 3 percent, both compounded annually. Treat the Canadian dollar as the domestic currency.

a. What is the estimated value of this put option by using the binomial model?

b. Calculate the estimated value of this put option for U.S. T-Bill rates of 0%, 1%, 2%, 4%, 5%, and 6%. Plot these values in a graph (by hand or using Excel), with put option values on the y-axis and U.S. T-bill rates on the x-axis. What can we conclude about the relationship between foreign interest rates and foreign currency put option values?

c. Calculate the estimated value of this put option for Canadian T-Bill rates of 0%, 1%, 2%, 4%, 5%, and 6%. Plot these values in a graph (by hand or using Excel), with put option values on the y-axis and Canadian T-bill rates on the x-axis. What can we conclude about the relationship between domestic interest rates and foreign currency put option values?

Question 4. Option Pricing with Black-Scholes-Merton Model

Today is January 12, 2017. The shares of XYZ Inc. are currently selling for $120 per share. The shares have an estimated volatility of 25%. XYZ Inc. is also expected to pay a dividend of $1.50 with an ex-dividend date of January 25, 2017. The risk-free rate is 6.17 percent per year with continuous compounding. Assume that one call option gives the holder the right to purchase one share.

a. Use the Black-Scholes-Merton model to estimate the fair value of a European call option on XYZ shares, with exercise price of $125 and expiration date of March 21, 2017. (Note that 2017 is not a leap year.)

b. This European call option has a market price of $3.00. Is it correctly priced? If not, how can an investor use the put-call parity to take advantage of this arbitrage opportunity?

Question 5. Volatility and Option Hedging

Today, is January 4, 2016. IBM common stock is selling at $135.95 per share. The stock has a dividend yield of 4% per year. The following table contains the monthly stock prices for IBM shares during the last 12 months.

Month (2015)	IBM Share Price
January	148.46
February	157.92
March	156.51
April	167.04
May	166.69
June	159.82
July	159.16
August	146.52
September	143.62
October	138.78
November	139.42
December	137.62

A call option with a March 18, 2016 expiration date and an exercise price of $130 is currently trading at $6.50. Each option entitles the holder to purchase 100 IBM shares. The risk-free rate is 0.58%, compounded continuously. Shares and options can only be bought and sold in whole numbers. Note that 2016 is a leap year.

a. Compute the historical volatility in terms of annualized standard deviation on the IBM shares, using the 12-month price data in the table above. Note that the volatility should be calculated on the stock returns and not on the stock prices. Obtain your answer to four decimal places (or two decimal places in percentage).

b. Based on the market price of $6.50, derive the implied volatility on the IBM shares. You may use the BlackScholesMertonImpliedVolatility10e.xlsm file provided by the textbook's authors to derive the implied volatility. Take a screen shot of the answer provided in this Excel spreadsheet, and copy and paste it into your answer for this question. Obtain your answer to four decimal places (or two decimal places in percentage).

c. Construct a delta-hedge position on January 4, 2016 involving the sale of 1,000 calls. Then rebalance the portfolio at the end of the next day, when the share price goes down to $135 per share. Assume the market call price is correct. That is, use the implied volatility as the correct volatility for the IBM shares. (You may calculate the deltas using the formula or the BlackScholesMertonBinomial10e.xlsm file provided by the textbook's authors. If you use the latter, include a screen shot of the Excel spreadsheet in your answer.)

Obtain the value of this delta-hedge portfolio after it has been rebalanced. Compare this value to the target value of the portfolio should its initial value be invested at the risk-free rate. Explain the difference.

d. There is another call option on IBM shares with an exercise price of $125 and the same expiration date (March 18, 2016). Construct a delta- and gamma-hedge portfolio on January 4, 2016 involving the sale of 1,000 of the 130-call option. Then rebalance the portfolio at the end of the next day, when the share price goes down to $135 per share. Again, use the implied volatility as the correct volatility for the IBM shares. (You may calculate the deltas and gammas using the formula or the BlackScholesMertonBinomial10e.xlsm file provided by the textbook's authors. If you use the latter, include a screen shot of the Excel spreadsheet in your answer.)

Obtain the value of this delta-and-gamma-hedged portfolio after it has been rebalanced. Compare this value to the target value of the portfolio should its initial value be invested at the risk-free rate. Explain the difference.

e. Explain the difference between the delta-hedged portfolio value in part (c) and the delta-and-gamma-hedged portfolio value in part (d).

Question 6. Protective Put

Suncor Energy Inc. (SU) shares are listed on the New York Stock Exchange. At 9:30 a.m. on January 14, 2016, these shares sold for $21.85 per share. The volatility on the returns of Suncor shares is approximately 24%. The following call and put option contracts were available for the months of January, February, and March:

	CALLS
Strike/Expiry	January 22, 2016	February 19, 2016	March 18, 2016
23	0.34	0.72	0.96
24	0.13	0.41	0.69
25	0.25	0.26	0.40

	PUTS
Strike/Expiry	January 22, 2016	February 19, 2016	March 18, 2016
23	1.28	2.01	2.14
24	2.63	2.80	2.92
25	3.60	3.70	3.95

Each option contract involves 100 shares. The risk-free rates for these three expiration dates are 0.6%, 1%, and 1.2%. All three rates are continuously compounded.

Given the information on Suncor shares and options above, construct a protective put using the 23-put with February expiration. Hold the protective put position until expiration.

a. Write out the payoff and profit function.

b. Use a table to show the payoffs and profits when the put option expires in-the-money and out-of-the-money.

c. Calculate the potential profits for this protective put, using share prices ranging from 0 to 26. Plot a graph of these potential profits, with share prices on the x-axis, and profits on the y-axis.

d. What is the breakeven share price at expiration for this protective put?

e. What is the maximum profit and maximum loss on this protective put?

Question 7. Box Spread

Use the data on Suncor Inc. presented in Question 6 above to answer this question.

a. Construct a box-spread using the March option contracts with exercise prices of 24 and 25.

b. Construct a profitable riskless arbitrage opportunity using this box-spread, with the requirement of $0 investment today. Calculate the NPV of the riskless profit.

Question 8. Futures Pricing Assumptions

What are the assumptions that allow us to obtain the prices of futures and forward contracts in the same way? What happens if these assumptions are not satisfied?

Question 9. Contango and Backwardation

a. Define and contrast contango and normal contango.

b. Define and contrast backwardation and normal backwardation.

c. Explain the relationship between contango, cost-of-carry, and convenience yield.

d. Explain the relationship between backwardation, cost-of-carry, and convenience yield.

Question 10. Stock Futures with Dividends

Today is January 3. Your friend David has just bought a futures contract on a stock index, and the contract specifies one year to expiration. The current share price is $80, and the annually compounded interest rate is 10%. The stock will pay quarterly dividends of $2 during the next year, with dividends payments on the following dates:

January 25

April 25

July 25

October 25

Assume that this is a non-leap year.

a. What is the futures price on this contract on January 3?

b. What is the cost-of-carry on this futures contract on January 3?

c. What is the value of this futures contract on February 17 if the spot price turns out to be $90 on that day?

d. Suppose that, instead of paying a quarterly dividend of $2, the stock index has an annual dividend yield of 10%. The continuously compounded interest rate is 10.52%. What is the price of the index futures on January 3? What is its value on February 17 when the index turns out to be $90?

Question 11. Put-Call Parity for Options on Futures

The spot price of corn is 301.40 cents per bushel. The three-month futures price on corn is 316.2 cents per bushel. The two-month call option on this corn futures with an exercise price of 330 cents per bushel is priced at $3.50. The two-month put option on this corn futures with an exercise price of 330 cents per bushel is priced at $12.70. The continuously compounded risk-free rate is 2.3%. Construct a risk-free arbitrage strategy with positive cash flow at time 0 and zero cash flow at the option expiration time T. Show the time 0 and time T cash flows in two separate tables.

Question 12. Pricing Option on Futures

Today is September 1. A futures contract on crude oil expiring on December 20 of the same year has a futures price of $44.70. The volatility on the futures contract is 23%, and the continuously compounded risk-free rate is 2%. Assume that there are 365 days in a year.

a. What is the Black model price of a European call option on this futures contract, expiring on October 17 and with an exercise price of $46?

b. What is the Black model price of a European put option on this futures contract, expiring on December 20 and with an exercise price of $50?

Question 13. Foreign Currency Futures and Arbitrage Strategy

Today is May 23, 2016. The spot rate for British pounds is 1.9032 CAD/£. The Canadian risk-free rate is 0.52%, and the British risk-free rate is 0.45%. Both risk-free rates are compounded continuously. The vote by the British population for U.K. exit from the European Union (commonly referred to as Brexit) will occur in exactly one month. Due to the uncertainty from this event, market volatility on the British pounds futures is quite high. As an example, the British pound futures contract, which expires on September 23, is priced below the spot rate at 1.4497CAD/£. The futures contract size is 62,500 British pounds. Is the futures contract incorrectly priced? If so, construct a risk-free arbitrage strategy to take advantage of the mispricing. Assume there are 365 days in the year, and the Canadian dollar is the domestic currency.

Question 14. Fed Funds Futures Arbitrage

On August 1, the one-month LIBOR rate is 2.0 percent and the two-month LIBOR rate is 2.5 percent. The 30-day fed funds futures is quoted at 96.75. Assuming no basis risk between fed funds and one-month LIBOR at the start of the delivery month, identify whether an arbitrage opportunity is available. The contract size of the fed funds futures is $5,000,000.

Question 15. Cheapest-to-Deliver Bond

Today is July 1. You hold a November Treasury bond futures contract with a price of 92:15 (i.e., 92 plus [15/32]), with a delivery date of November 15 in the same year. You have identified the two bonds below that could be used for delivery against the futures contract:

	Bond A	Bond B
Maturity	26.5 years	31 years
Coupon rate	5%	8.5%
Asking price	93:2	144:13
Coupon dates	April 15, October 15	June 15, December 15
Callable?	No	No

Assume that the next year is not a leap year, and that the market repo rate is 5.50%.

a. Find the conversion factors for Bond A and Bond B. Use the downloadable Excel spreadsheet on the Chicago Mercantile Exchange (CME) website: https://www.cmegroup.com/trading/interest-rates/us-treasury-futures-conversion-factor-lookup-tables.html.

b. Identify the cheapest-to-deliver bond.

Question 16. Price Sensitivity Hedge

Mr. Toriop manages a bond portfolio valued at $27,492,045. The bonds in this portfolio have a face value of $25 million. The portfolio has a yield of 8.35 percent and a duration of 7.67. Mr. Toriop is worried that interest rates will rise within the next year. He would like to lower the duration of your bond portfolio to 5 years. He finds a one-year bond futures contract and thinks that it would be an appropriate hedge for your portfolio. This futures contract is priced at 109 17/32, has an implied yield of 8 percent, and has an implied duration of 7.9 years.

The futures contract size is $100,000.

a. Should Mr. Toriop buy or sell futures?
b. How many contracts should Mr. Toriop use?

c. Suppose that the portfolio's value falls to $26,557,089, and the futures price turns out to be 103 8/32 in one year's time. What is the net profit from the hedged position?

d. If Mr. Toriop were to liquidate the entire bond portfolio in one year's time given the information in part (c), what would be the total proceeds received?

Question 17. Minimum Variance Commodity Hedge

Choc Full of Good Inc., a producer of powdered hot chocolate, has just received a large order that will require the purchase of 800 metric tons of cocoa in 3 months. The current spot price of cocoa is US $3,055 per metric ton. The standard deviation of the change in spot cocoa price is 0.2. Mr. Dulce, the CFO of Choc Full, is considering a minimum-variance hedge of this future cocoa purchase using the three-month cocoa futures contract. The contract size is 10 metric tons. The standard deviation of the change in cocoa futures price is 0.25. The covariance between the change in the spot and futures cocoa price is 0.035. The annually compounded interest rate faced by the company is 5%, the three-month storage cost is $2.5 per metric ton, and the convenience yield is $0.5 per metric ton.

a. What is the futures price per metric ton of cocoa?

b. Should the company long or short cocoa futures?

c. Compute the minimum-variance hedge ratio.

d. How many contracts should be traded?

e. What is the estimated effectiveness of this minimum variance hedge?

f. What is the correlation of the change in the spot and futures cocoa price?

g. What is the profit from this hedged position if the spot cocoa price in three months turns out to be $3,100?

h. Calculate the gain/loss on spot position, the gain/loss on futures position, and the profits from this hedged position by hypothesizing that the spot cocoa price in three months will range from $2,900 to $3,200, with increments of $25. Plot these numbers on a graph. Explain what you see from the graph in terms of the relationship between the gain/loss on spot position, gain/loss on futures position, and hedged profits/losses. (Hint: Use an Excel spreadsheet to do this one.)

Question 18. Hedging with Stock Index Futures

You manage a portfolio that is currently all invested in equities in companies in five major Canadian industries. The market value involved and beta for each industry are shown in the table below.

Industry	Market Value	Beta
Oil and Gas	$1,100,000	1.2
Technology	900,000	1.5
Utilities	1,500,000	0.8
Financial	1,000,000	1.3
Pharmaceutical	800,000	1.1

You believe that the Canadian equity market is on the verge of a big but short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs of liquidating and re-establishing your equity position. Instead, you decide to hedge your portfolio with three-month S&P/TSX 60 index futures contracts for one month. Currently, the level of the S&P/TSX 60 index is 851.38, the three-month futures price of the S&P/TSX 60 is 856.40, and one contract is for $200 times the index. The annual simple risk-free rate of return is 1%.

a. Should you long or short the S&P/TSX 60 futures?

b. How many futures contracts should you use?

c. Suppose the return on the S&P/TSX 60 index is -5% in one month, and the S&P/TSX index futures price falls to 830 in one month. Calculate your net gain or loss on your hedged portfolio in part (a). (Hint: Use the CAPM formula to derive the portfolio return. Then use the portfolio return to obtain gain/loss on the portfolio).

Question 19. Plain Vanilla Interest Rate Swap

Incredible Inc., a manufacturer of children's toys, enters into a two-year plain vanilla interest rate swap, in which the corporation will receive a fixed rate and pay a floating rate of LIBOR. The notional amount on this swap is $75 million. Swap payments will be netted every 180 days, and the LIBOR requires the assumption of a 360-day year. The term structure of LIBOR on the swap initiation date is as follows:

Days	Rate (%)
180	3.50
360	3.55
540	3.60
720	3.70

a. What is the fixed rate determined on the swap initiation date?

b. Calculate the swap value on the initiation date.

c. What is the first net payment on the swap? Who makes this payment, Incredible Inc. or the swap dealer?

d. Assume that it is now 120 days into the life of the swap. The new term structure of LIBOR is as follows:

Days	Rate (%)
60	3.60
240	3.70
420	3.80
600	3.90

Calculate the value of the swap on Day 120.

e. Assume that it is now 360 days into the life of the swap. The new term structure of LIBOR is as follows:

Days	Rate (%)
180	3.85
360	3.90
540	3.95
720	4.00

Calculate the net payment on the swap on Day 540, and the value of the swap on Day 360.

Question 20. Currency Swap

A Canadian corporation (ACC) has just entered into a two-year currency swap contract with Big Dealer Bank (BDB). The swap contract requires ACC to make semi-annual payments in Canadian dollars (C$) and receive semi-annual payments in U.S. dollars (US$). The notional amount in Canadian dollars is C$25 million. The accrual period for the swap is 180/360, assuming 360 days per year. The US$/C$ spot exchange rate is 0.77, with the Canadian dollar being the domestic currency for ACC. The term structures of C$ LIBOR and US$ LIBOR are as follows:

Days	C$ LIBOR (%)	US$ LIBOR (%)
180	0.50	0.55
360	0.60	0.65
540	0.65	0.75
720	0.70	0.85

a. What is the notional amount in U.S. dollars?

b. Calculate the fixed rates in Canadian and U.S. dollars.

c. Calculate the first semi-annual payments for the swap if the terms of the swap specify that ACC receives fixed rates and pays floating rates.

d. What is the value of the currency swap at the time of contract initiation?

e. Assume 240 days has passed since the initiation of the currency swap contract. The new exchange rate is US$0.85/C$. Calculate the value of the swap given the following LIBOR term structures at time 240.

Days	C$ LIBOR (%)	US$ LIBOR (%)
120	0.60	0.60
300	0.70	0.65
480	0.80	0.70
660	0.90	0.80

Question 21. FRA Pricing, Valuation, Payoff, and Hedging

Today is June 1. Sustainable Corporation has an obligation of $25 million coming due on August 1. The company is planning to borrow this amount on August 1 to fulfill its obligation, and plans to pay back the loan on December 1. The company's borrowing rate is LIBOR + 125 basis points. The company's bank presents it with the following LIBOR term structure:

# days	LIBOR
30	0.90%
60	1.00%
90	1.05%
120	1.10%
150	1.15%
180	1.18%
210	1.20%
240	1.21%

For the calculation of interest, the bank assumes 30 days in a month, and 360 days in a year.

Ms. Devro, the VP Finance of Sustainable, is worried that LIBOR will increase between June and August, thus increasing the company's borrowing cost. She advises that the company enters into a forward rate agreement (FRA) with its bank to hedge its interest rate risk. She has asked you, the treasurer of the company, to present her with answers to the following questions:

a. Should Sustainable take a long or short position in the FRA?

b. What is the fixed rate on the FRA, based on the LIBOR term structure provided by the bank?

c. July 1 is the end of the company's third quarter of operations, and the company must estimate the fair value of all its contracts, including derivatives, for its quarterly financial statements. What is the value of this FRA if the LIBOR term structure turns out to be the following on July 1?

# days	LIBOR
30	0.90% + 0.50%
60	1.00% + 0.50%
90	1.05% + 0.50%
120	1.10% + 0.55%
150	1.15% + 0.55%
180	1.18% + 0.55%
210	1.20% + 0.60%
240	1.21% + 0.60%

d. What will be the payoff on the FRA on August 1 if the company's business analysts expect the LIBOR term structure to turn out to be the following when the FRA expires?

# days	LIBOR
30	0.90% + 0.50%
60	1.00% + 0.50%
90	1.05% + 0.50%
120	1.10% + 0.55%
150	1.15% + 0.55%
180	1.18% + 0.55%
210	1.20% + 0.60%
240	1.21% + 0.60%

e. Given the LIBOR term structure given for August 1 in Question 3, what are the effective annual rates with and without the FRA hedge? For compounding interest calculations, the company uses 365 days per year.

f. Should Sustainable hedge its interest rate risk with this FRA?

Question 22. Interest Rate Options - Pricing, Valuation, Payoff, and Hedging

Tango Bank has contracted to lend $80 million to Delta Co. in three months' time. This loan will be for a period of six months. To hedge against the risk of interest rates dropping, Tango has purchased an interest rate put option. The put option has an exercise rate of 2.15% and a maturity of three months. The underlying forward rate is based on the LIBOR, which has a current term structure of

# days	LIBOR
90	2%
270	2.3%

The terms of the LIBOR specify 30 days in a month and 360 days in a year. The volatility on the underlying forward rate is 0.25. Tango uses the Black Model to estimate the call premium.

a. Calculate the contract premium the bank must pay for this put option.

b. Suppose that in three months' time, the six-month LIBOR turns out to be 2%. What is the annualized rate of return on Tango's position with the put option?

c. Hindsight being 20-20, should Tango have purchased the put option?

d. Tango could also have used a forward rate agreement (FRA) to hedge its future lending rate. What are the similarities and differences between interest rate option and FRA?

Question 23. Delta Hedging

A portfolio consists of 1,000 shares of stock and 500 short calls on that stock. The current stock price is $92.20. The call option has a maturity of one year, with an exercise price of $100 and a standard deviation of 25%. The risk-free rate is 5%. The call option price is found by using the Black-Merton-Scholes model. What would be the dollar change in the value of the portfolio be in response to a one-dollar increase in the stock price?

Question 24. VAR Calculation

A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an annual expected return of 15% and annual volatility of 20%. The firm has a position of $100 million in stock A. Stock B has an annual expected return of 25% and an annual volatility of 30% as well. The firm has a position of $50 million in stock B. The correlation coefficient between the returns of these two stocks is 0.3.

a. Compute the 5% annual VAR for the portfolio. Interpret the resulting VAR.

b. What is the 5% daily VAR for the portfolio? Assume 365 days per year.

c. If the firm sells $10 million of stock A and buys $10 million of stock B, by how much does the 5% annual VAR change?